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The stepped reckoner or Leibniz calculator was a mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz (started in 1673, when he presented a wooden model to the Royal Society of London [2] and completed in 1694). [1]
The naturalness of the star operator means it can play a role in differential geometry, when applied to the cotangent bundle of a pseudo-Riemannian manifold, and hence to differential k-forms. This allows the definition of the codifferential as the Hodge adjoint of the exterior derivative , leading to the Laplace–de Rham operator .
Since they lie on a parabola, which is a convex curve, it is easy to see that the vertices of the convex hull, when traversed along the boundary, produce the sorted order of the numbers , …,. Clearly, linear time is required for the described transformation of numbers into points and then extracting their sorted order.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.
If the boundary of Ω is C k for k ≥ 2 (see Differentiability classes) then d is C k on points sufficiently close to the boundary of Ω. [3] In particular, on the boundary f satisfies = (), where N is the inward normal vector field. The signed distance function is thus a differentiable extension of the normal vector field.
Mathematically, shape optimization can be posed as the problem of finding a bounded set, minimizing a functional (),possibly subject to a constraint of the form =Usually we are interested in sets which are Lipschitz or C 1 boundary and consist of finitely many components, which is a way of saying that we would like to find a rather pleasing shape as a solution, not some jumble of rough bits ...
When two cells in the Voronoi diagram share a boundary, it is a line segment, ray, or line, consisting of all the points in the plane that are equidistant to their two nearest sites. The vertices of the diagram, where three or more of these boundaries meet, are the points that have three or more equally distant nearest sites.